Membranes composed of multilayer poly(4-styrenesulfonate) (PSS)/protonated poly(allylamine) (PAH) films on porous alumina supports exhibit high monovalent/divalent cation selectivities. Remarkably, the diffusion dialysis K(+)/Mg(2+) selectivity is >350. However, in nanofiltration this selectivity is only 16, suggesting some convective ion transport through film imperfections. Under MgCl(2) concentration gradients across either (PSS/PAH)(4)- or (PSS/PAH)(4)PSS-coated alumina, transmembrane potentials indicate Mg(2+) transference numbers approaching 0. The low Mg(2+) transference numbers with both polycation- and polyanion-terminated films likely stem from exclusion of Mg(2+) due to its large size or hydration energy. However, these high anion/cation selectivities decrease as the solution ionic strength increases. In nanofiltration, the high asymmetry of membrane permeabilities to Mg(2+) and Cl(-) creates transmembrane diffusion potentials that lead to negative rejections (the ion concentration in the permeate is larger than in the feed) as low as -200% for trace monovalent cations such as K(+) and Cs(+). Moreover, rejection becomes more negative as the mobility of the trace cation increases. Knowledge of single-ion permeabilities is vital for predicting the performance of polyelectrolyte films in the separation and purification of mixed salts.